Abstract
Community detection is one of the most important problems in the field of complex networks in recent years. The majority of present algorithms only find disjoint communities, however, community often overlap to some extent in many real-world networks. In this paper, an improved multi-objective quantum-behaved particle swarm optimization (IMOQPSO) based on spectral-clustering is proposed to detect the overlapping community structure in complex networks. Firstly, the line graph of the graph modeling the network is formed, and a spectral method is employed to extract the spectral information of the line graph. Secondly, IMOQPSO is employed to solve the multi-objective optimization problem so as to resolve the separated community structure in the line graph which corresponding to the overlapping community structure in the graph presenting the network. Finally, a fine-tuning strategy is adopted to improve the accuracy of community detection. The experiments on both synthetic and real-world networks demonstrate our method achieves cover results which fit the real situation in an even better fashion.
Similar content being viewed by others
References
Broder, A., Kumar, R., Maghoul, F.: Graph structure in the Web: experiments and models. Comput. Netw. 33(1–6), 309–320 (2000)
Capocci, A., Servedio, V., Caldarelli, G., Colaiori, F.: Detecting communities in large networks. Physica A 352(2–4), 669–676 (2005)
Carlos, A., Coello, Coello, et al.: Handling multiple objectives with particle swarm optimization. IEEE Trans. Evolut. Comput. 8(3), 256–279 (2004)
Chen, Y.Z., Gao, Y.L.: An improved adaptive harmony search algorithm. J. Gansu Lianhe Univ. (Nat. Sci.) 25(2), 63–66 (2011)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGAII. IEEE Trans. Evolut. Comput. 6(2), 182–197 (2002)
Dorogovtsev, S.N., Mendes, F., Samukhin, A.N.: Structure of growing networks with preferential linking. Phys. Rev. Lett. 85(21), 4633–4636 (2000)
Duan, X.D., Wang, C.R., Liu, X.D., Lin, Y.P.: Web community detection model using particle swarm optimization. In IEEE Congress on Evolutionary Computation, pp. 1074–1079 (2010)
Duch, J., Arenas, A.: Community detection in complex networks using extremal optimization. Phys. Rev. E 72(2), 027104 (2005)
Geem, Z.W., Kim, J.H., Loganathan, G.V.: A new heuristic optimization algorithm: harmony search. Simulation 76(2), 60–68 (2001)
Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. 99(12), 7821–7826 (2002)
Gregory, S.: A fast algorithm to find overlapping communities in networks. In Proceedings of the 12th European Conference of Knowledge Discovery in Databases, vol. 5211, pp. 408–423 (2008)
Huang, Z., Wang, Y.J., Yang, C.J., Wu, C.Z.: A new improved quantum-behaved particle swarm optimization model. In: IEEE Conference on Industrial Electronics and Applications, pp. 1560–1564 (2009)
Jiao, L.C., Li, Y.Y., Gong, M.G., Zhang, X.R.: Quantum-inspired immune clonal algorithm for global optimization. IEEE Trans. Syst. Man Cybern. B 38(5), 1234–1253 (2008)
Lancichinetti, A., Fortunato, S.: Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. Phys. Rev. E 80(1), 016118 (2004)
Lancichinetti, A., Fortunato, S., Kertesz, J.: Detecting the overlapping and hierarchical community structure of complex networks. New J. Phys. 11, 033015 (2009)
Li, Y.Y., Xiang, R.R., Jiao, L.C., Liu, R.C.: An improved cooperative quantum-behaved particle swarm optimization. Soft Comput. 16, 1061–1069 (2012)
Liu, X., Li, D., Wang, S., Tao, Z.: Effective algorithm for detecting community structure in complex networks based on GA and clustering. In Proceedings of the 7th International Conference on Computational Science, pp. 657–664 (2007)
Liu, J., Zhong, W.C., Abbass, H.A., Green, D.G.: Separated and overlapping community detection in complex networks using multiobjective evolutionary algorithms. In Proceedings of IEEE Congress on Evolutionary Computation, pp. 1–7 (2010)
Liu, T., Hu, B.Q.: Detecting community in complex networks using cluster analysis. Complex Syst. Complex. Sci. 4(1), 28–35 (2007)
Liu, J., Liu, T.Z.: Detecting community structure in complex networks using simulated annealing with k-means algorithms. Physica A 389(11), 2300–2309 (2010)
Lusseau, D., Schneider, K., Boisseau, O.J., Haase, P., Slooten, E., Dawson, S.M.: The bottlenose dolphin community of doubtful sound features a large proportion of long-lasting associations. Behav. Ecol. Sociobiol. 54(4), 396–405 (2003)
Mahdavi, M., Fesanghary, M., Damangir, E.: An improved harmony search algorithm for solving optimization problem. Appl. Math. Comput. 188(2), 1567–1597 (2007)
Milgram, S.: The small world problem. Psychol. Today 1(1), 61–67 (1967)
Newman, M.E.J.: Fast algorithm for detecting community structure in networks. Phys. Rev. E 69(6), 066133 (2004)
Newman, M.E.J.: Modularity and community structure in networks. Proc. Natl. Acad. Sci. 103(23), 8577–8582 (2006)
Palla, G., Derenyi, I., Farkas, I., Vicsek, T.: Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 814–818 (2005)
Pereira, J.B., Enright, A.J., Ouzounis, C.A.: Detecion of functional modules from protein interaction networks. Proteins 54(1), 49–57 (2004)
Pizzuti, C.: GA-Net: a genetic algorithm for community detection in social networks. In Proceedings of the 10th Intenational Conference on Parallel Problem Solving from Nature, pp. 1081–1090 (2008)
Pizzuti, C.: Overlapped community detection in complex networks. In Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation, pp. 859–866 (2009)
Pool, I., Kochen, M.: Contacts and influence. Soc. Netw. 1(1), 5–51 (1978)
Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., Parisi, D.: Defining and identifying communities in networks. Proc. Natl. Acad. Sci. 101(9), 2658–2663 (2004)
Shen, H.W., Cheng, X.Q., Cai, K., Hu, M.B.: Detecting overlapping and hierarchical community structure in networks. Physica A 388, 1706–1712 (2009)
Shi, C., Zhong, C., Yan, Z.Y. et al., A Multi-objective optimization approach for community detection. In IEEE Congress on Evolutionary Computation, pp. 1–8 (2010)
Shi, Z.W., Liu, Y., Liang, J.J.: PSO-based Community detection in complex networks. Second Int. Symp. Knowl. Acquis. Model. 3, 114–119 (2009)
Sun, J., Feng, B., Xu, W.B.: Particle swarm optimization with particles having quantum behavior. Proc. IEEE Congr. Evolut. Comput. 1, 325–331 (2004)
Tasgin, M., Bingol, H.: Community detection in complex networks using genetic algorithm. Condens. Matter, 0604419 (2006)
Wang, X.H., Jiao, L.C., Wu, J.S.: Adjusting from disjoint to overlapping community detection of complex networks. Physica A 388(24), 5045–5056 (2009)
Wu, T., Shi, L.Y., Geunes, J., Akartunali, K.: An HNP–MP approach for the capacitated multi-item lot sizing problem with setup times. IEEE Trans. Autom. Sci. Eng. 7(3), 500–511 (2010)
Wu, T., Shi, L.Y., Geunes, J., Akartunali, K.: An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging. Eur. J. Oper. Res. 214(2), 428–441 (2011)
Xi, M.L., Sun, J., Xu, W.B.: An improved quantum-behaved particle swarm optimization algorithm with weighted mean best position. Appl. Math. Comput. 205(2), 751–759 (2008)
Zachary, W.W.: An information flow model for conflict and fission in small groups. J. Anthropol. Res. 33(4), 452–473 (1977)
Zhang, S., Wang, R.S., Zhang, X.S.: Identification of overlapping community structure in complex networks using fuzzy c-means clustering. Physica A 374, 483–490 (2007)
Acknowledgments
This work was supported by the Program for New Century Excellent Talents in University (No. NCET-12-0920), the Program for New Scientific and Technological Star of Shaanxi Province (No. 2014KJXX-45), the National Natural Science Foundation of China (Nos. 61272279, 61272282, 61371201 and 61203303), the Fundamental Research Funds for the Central Universities (Nos. K5051302049, K5051302023, K50511020011, K5051302002 and K5051302028), the Provincial Natural Science Foundation of Shaanxi of China (No. 2011JQ8020), the Fund for Foreign Scholars in University Research and Teaching Programs (the 111 Project) (No. B07048) and EU IRSES project (No. 247619).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, Y., Wang, Y., Chen, J. et al. Overlapping community detection through an improved multi-objective quantum-behaved particle swarm optimization. J Heuristics 21, 549–575 (2015). https://doi.org/10.1007/s10732-015-9289-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10732-015-9289-y